Motion -CBSE CLASS 9

Motion

CONTENT LIST

Describing Motion

Motion:- If an object changes it's position with respect to time then it is said to be in motion
Rest:- If an object doesn't change it's position with respect to time then it is said to be in motion

There are many types of motion:-

Rectilinear Motion :- If an object moves along a straight line then it is said to be object is in rectilinear motion.
Curvilinear Motion:- If an object moves along a curve line then it is said to be object is in curvilinear motion.
Oscillatory Motion:- If an object performes to and fro movement about a fixed point then it is said to be in Oscillatory motion
Circular Motion:- If an object moves along a circular path then it is said to be object is in circular motion.
Rotational Motion:- If an object moves along a circular path about a fixed axis then it is said to be object is in Rotational motion.
Periodic Motion:- If an object repeats it's path of motion after an interval of time then it is said to be in periodic motion.
Uniform motion:- If an object covers same distance in equal interval of time then it is said to ben in uniform motion.
Non- uniform motion:- If an object doesn't covers same distance in equal interval of time then it is said to ben in non- uniform motion.
Random Motion:- If an object doesn't move along a fixed path then it is said to be in random motion.
Vibratory motion:- If an object performes to and fro movement about a fixed point then it is said to be in Vibratory motion

DISTANCE

When object is in motion or changes its position ,It follows certain path.
The length of path followed by object doing motion is called distance.
A cyclist moves from A to B and to C, distance travelled is AB+BC=4+3=7m

DISPLACEMENT

When object is in motion or changes its position ,The shortest distance between initial and final position is called displacement.
A cyclist moves from A to B and to C, distance travelled is AB.+BC=4+3=7m.
Cyclist moves from A (initial position)to C (final position).
AC=5m is the shortest distance between A and C is called displacement.

TYPES OF DISPLACEMENT:-

DIFFERENCE BETWEEN DISTANCE AND DISPLACEMENT:-

UNIFORM MOTION AND NON-UNIFORM MOTION

Uniform-motion:-If an object covers same distance in equal interval of time then it is said to ben in uniform motion.
Non-Uniform-motion:-If an object doesn't covers same distance in equal interval of time then it is said to ben in non- uniform motion.

Measuring the Rate of Motion

SPEED

Distance travelled by an object in unit time is called speed.
The SI unit of Speed is meter/second (m/s).
Speed is a scalar quantity.
Speed = distance / time
There are two type of speed :-

Uniform Speed:- An object is said to be moving with a Uniform or non-variable speed if it covers equal distance in equal interval of time. eg- The motion of a ball on a frictionless surface is with uniform speed.
Non-Uniform Speed:- An object is said to be moving with a non- uniform or variable speed if it covers un-equal distance in equal interval of time. eg- The motion of a ball on a rough surface and motion of a car in crowded street.

AVERAGE SPEED:-
The ratio of total distance travelled by the object to the total time journey is called it's average speed.
it's formula is :-
Average speed= total distance/total time.

SPEED WITH DIRECTION

Speed with direction is called velocity. or, distance travelled by an object in unit time with given direction then it is called velocity.
The SI unit of velocity is meter/second (m/s).
velocity is a vector quantity.
velocity = displacement / time
There are two type of speed :-

Uniform Velocity:- An object is said to be moving with a Uniform or non-variable velocity if it covers equal distance in equal interval of time.
Non-Uniform Velocity:- An object is said to be moving with a non- uniform or variable velocity if it covers un-equal distance in equal interval of time.

AVERAGE VELOCITY:-
If the velocity
it's formula is :-
Average speed= total distance/total time.

Rate of Change of Velocity

During uniform motion of an object along a straight line, the velocity of object remains constant with time. In this case, the change in velocity of the object for any time interval is zero.

In non-uniform motion, velocity changes with time. It has different values at different instants and at different points of the path. Thus, the change in velocity of the object during any time interval is not zero. Here another physical quantity is taken into consideration and it is called acceleration.

Acceleration is a measure of the change in the velocity of an object per unit time.

If the velocity of an object changes from an initial value u to the final value v in time t,the acceleration is

a = (v–u)

We can says Rate of Change of Velocity is equal to acceleretion of object.

If an object travels in a straight line and its velocity increases or decreases by equal amounts in equal intervals of time, then the acceleration of the object is said to be uniform. An object freely falling due to garvitational force is an example of uniform accelaeration.

If an object travels with non-uniform acceleration if its velocity changes at a non-uniform rate.

Graphical Representation of Motion

DISTANCE–TIME GRAPHS

consider a car is moving with a constant speed covering 50km in every 20 minutes, as shown in below table.

When we plot the graph of moving car by taking distance covered along y axis and time on covered along x axis, the distance-time graph will be as below

The above graph shows uniform speed. The slope here shows the speed of the object, like if the slop is stiff then the speed is more and if the slope is not stiff then it has low speed.

The above graph shows non-uniform speed. Distance is taken on x-axis and time is taken on y-axis in accordance to time distance is not covered equally so the graph doesn't go in a straight line and goes in curve line.

VELOCITY-TIME GRAPHS

The above graph shows object moving with constan velocity. Here, velocity is taken on y-axis and time is taken on x-axis as time passes the object is moving with same velocity, so the line goes parallel to the x-axis From origin to time 't' it is the same velocity.
Area covered by the graph is displacement as (velocity x time = displacement). For example:-

Here, we have to find the displacement.

The graph for the following:

given,
base which is 0.6s,
height is 6m/s
displacement= velocity * time
But, here it will displacement = 1/2 * velocity * time
=> 1/2 * (6m/s) * (0.6sec)
=> 1/2 * 6/1 * 6/10
=> 18/10 = 1.8m
Here the displacement is 1.8m

Equations of Motion by Graphical Method

1^st equation of Motion:-

The points A and B on the graph correspond to times 0 and t respectively.
The velocity of the object at time t = 0 , is u (intial velocity) as represented by OA in the graph.
The velocity of the object at time t = t , is v (final velocity) as represented by OD in the graph.
Now take the perpendiculer BE on x-axis and also perpenducleur AC on BE.
The slope of velocity -time graph will give the accleration(a) of the object.
The slope of line AB = BC/AC
a = (BE-CE)/OE
a = (OD-OA)/OE
a = (v-u)/t
at = v-u
v = u + at

2^nd equation of Motion:-

The area under the velocity-time graph is equal to the displacement. In the time interval 0-t, the displacement is equal to the area of OABE.
s = area of OABE
s = area of the rectangle OACE + area of triangle ABC
s = (OA) - (OE) + 1/2 * (AC) * (BC)
s = (OA) - (OE) + 1/2 * (OE) * (BC/AC * AC)
s = (OA) - (OE) + 1/2 * (OE) * (BC/AC * OE)
s = (OA) - (OE) + 1/2(BC/AC) * OE²
OA = u, OE = t and BC/AC = slope = a. so
s = ut + 1/2at²

3^rd equation of Motion:-

The area of a trapezium = 1/2(sum of the parallel sides) x (distance between them).
So, the area of the trapezium OABE can be written as
s = 1/2(OA + EB) * (AC)
s = 1/2(OA + OD)* (AC/BC * BC)
s = 1/2(OA + OD) * (BE-CE/BC/AC)
s = 1/2(OD² - OA²/BC/AC)
s = 1/2(v² - u²/a)
2as = v² - u²
v² = u² + 2as

Circular Motion

When an object moves in circular path then it is said to be in circular motion.
Examples:- movment of fan, merry-go-rounds in parks, a car going around a roundabout, the moon orbiting around the Earth.

Uniform Circular Motion

If an object moves in a circular path with uniform speed then it is said to be moving in Uniform Circular Motion.
Example:- The moon orbiting around the Earth or the Earth revolving around the Sun.

The velocity of a body moving along a circular path changes continuously even if it is moving with uniform speed because direction of an object changes continuously.
The motion of an body moving along a circular path is accelerated motion since, it's velocity changes continuously
A centripetal force is net force that acts on any object to keep it moving in circulsr path. It acts inwards along the radius of circular path.
Any object moving along a circular path of radius r with velocity v experiences an acceleration directed toward the center of its path:- a = v²/r
Any object of mass 'm' moving along a circular path of radius r with velocity v experiences a force directed toward the center of its path:- f = mv²/r
An apparent force in outward direction is acting on the object moving on circular path. This force is called Centrifugal force.

Test your understanding

Question: A body is falling freely ,what remains the constant during the motion of body?

Answer: Acceleration as it is falling due to gravity (g=9.8 m/s2)

Question: Can distance is not zero even when displacement is zero?

Answer: Yes

Question: Can displacement is zero even when distance is not zero?

Answer: Yes

Question: A body moves over three quarter of a circle of radius "r". What is the magnitude of its displacement?

Answer:

Question: What will be the acceleration of body which is moving with uniform velocity?

Answer: zero because velocity is constant.

Question: Which quantity represent rate change of displacement?

Answer: velocity

Question: What is ratio of SI and CGS unit of displacement?

Answer: 100

Question: Can distance be negative?

Answer: No , distance cannot be negative.

Question: The motion of the Moon around the Earth in a circular path is an accelerated motion.Is is true or false?

Answer: True

Question: An artificial satellite revolves around the earth with a constant velocity.Is is true or false?

Answer: Velocity of setallite can not be constant as it is continiously changing its direction.

Question: Can magnitude of displacement of body be ever greater then distance travelled by body?

Answer: No

Question: The path of motion of an object under uniform motion may be straight, curve or circular. Is it true or false?